{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.2 线性回归的从零开始实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3.1\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "from IPython import display\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import random\n",
    "\n",
    "print(torch.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2.1 生成数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_inputs = 2\n",
    "num_examples = 1000\n",
    "true_w = [2, -3.4]\n",
    "true_b = 4.2\n",
    "features = torch.randn(num_examples, num_inputs,\n",
    "                      dtype=torch.float32)\n",
    "labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b\n",
    "labels += torch.tensor(np.random.normal(0, 0.01, size=labels.size()),\n",
    "                       dtype=torch.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.2427, -0.3207]) tensor(5.7937)\n"
     ]
    }
   ],
   "source": [
    "print(features[0], labels[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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   "source": [
    "def use_svg_display():\n",
    "    # 用矢量图显示\n",
    "    display.set_matplotlib_formats('svg')\n",
    "\n",
    "def set_figsize(figsize=(3.5, 2.5)):\n",
    "    use_svg_display()\n",
    "    # 设置图的尺寸\n",
    "    plt.rcParams['figure.figsize'] = figsize\n",
    "\n",
    "# # 在../d2lzh_pytorch里面添加上面两个函数后就可以这样导入\n",
    "# import sys\n",
    "# sys.path.append(\"..\")\n",
    "# from d2lzh_pytorch import * \n",
    "\n",
    "set_figsize()\n",
    "plt.scatter(features[:, 1].numpy(), labels.numpy(), 1);"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2.2 读取数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 本函数已保存在d2lzh包中方便以后使用\n",
    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))\n",
    "    random.shuffle(indices)  # 样本的读取顺序是随机的\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "        j = torch.LongTensor(indices[i: min(i + batch_size, num_examples)]) # 最后一次可能不足一个batch\n",
    "        yield  features.index_select(0, j), labels.index_select(0, j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 1.6760,  1.4384],\n",
      "        [-1.2412,  0.3110],\n",
      "        [-0.0490, -0.0988],\n",
      "        [-0.3068, -0.6336],\n",
      "        [ 0.8711, -0.5793],\n",
      "        [ 0.4112, -0.6168],\n",
      "        [-0.8340, -0.0621],\n",
      "        [ 0.1945, -1.6059],\n",
      "        [ 0.6881, -1.1369],\n",
      "        [-0.0081,  0.3313]]) \n",
      " tensor([ 2.6672,  0.6619,  4.4294,  5.7428,  7.9015,  7.1166,  2.7397, 10.0603,\n",
      "         9.4553,  3.0582])\n"
     ]
    }
   ],
   "source": [
    "batch_size = 10\n",
    "\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "    print(X, '\\n', y)\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2.3 初始化模型参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = torch.tensor(np.random.normal(0, 0.01, (num_inputs, 1)), dtype=torch.float32)\n",
    "b = torch.zeros(1, dtype=torch.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.], requires_grad=True)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w.requires_grad_(requires_grad=True)\n",
    "b.requires_grad_(requires_grad=True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2.4 定义模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linreg(X, w, b):  # 本函数已保存在d2lzh包中方便以后使用\n",
    "    return torch.mm(X, w) + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2.5 定义损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def squared_loss(y_hat, y):  # 本函数已保存在pytorch_d2lzh包中方便以后使用\n",
    "    return (y_hat - y.view(y_hat.size())) ** 2 / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2.6 定义优化算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sgd(params, lr, batch_size):  # 本函数已保存在d2lzh_pytorch包中方便以后使用\n",
    "    for param in params:\n",
    "        param.data -= lr * param.grad / batch_size # 注意这里更改param时用的param.data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2.7 训练模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.034421\n",
      "epoch 2, loss 0.000117\n",
      "epoch 3, loss 0.000052\n"
     ]
    }
   ],
   "source": [
    "lr = 0.03\n",
    "num_epochs = 3\n",
    "net = linreg\n",
    "loss = squared_loss\n",
    "\n",
    "for epoch in range(num_epochs):  # 训练模型一共需要num_epochs个迭代周期\n",
    "    # 在每一个迭代周期中，会使用训练数据集中所有样本一次（假设样本数能够被批量大小整除）。X\n",
    "    # 和y分别是小批量样本的特征和标签\n",
    "    for X, y in data_iter(batch_size, features, labels):\n",
    "        l = loss(net(X, w, b), y).sum()  # l是有关小批量X和y的损失\n",
    "        l.backward()  # 小批量的损失对模型参数求梯度\n",
    "        sgd([w, b], lr, batch_size)  # 使用小批量随机梯度下降迭代模型参数\n",
    "        \n",
    "        # 不要忘了梯度清零\n",
    "        w.grad.data.zero_()\n",
    "        b.grad.data.zero_()\n",
    "    train_l = loss(net(features, w, b), labels)\n",
    "    print('epoch %d, loss %f' % (epoch + 1, train_l.mean().item()))"
   ]
  },
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   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
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     "text": [
      "[2, -3.4] \n",
      " tensor([[ 1.9993],\n",
      "        [-3.3994]], requires_grad=True)\n",
      "4.2 \n",
      " tensor([4.2000], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "print(true_w, '\\n', w)\n",
    "print(true_b, '\\n', b)"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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   "source": []
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